Design for Lifecycle Cost Using Time-Dependent Reliability

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. As time progresses, the product may fail due to time phenomena such as time-dependent operating conditions, component degradation, etc. The degradation of reliability with time may increase the lifecycle cost due to potential warranty costs, repairs and loss of market share. In design for lifecycle cost, we must account for product quality, and time-dependent reliability. Quality is a measure of our confidence that the product conforms to specifications as it leaves the factory. Reliability depends on 1) the probability that the system will perform its intended function successfully for a specified interval of time (no hard failure), and 2) on the probability that the system response will not exceed an objectionable by the customer or operator, threshold for a certain time period (no soft failure). Quality is time-independent, and reliability is time-dependent. This article presents a design methodology to determine the optimal design of time-dependent, multi-response systems, by minimizing the cost during the life of the product. The conformance of multiple responses is treated in a series-system fashion. The lifecycle cost includes a production, an inspection, and an expected variable cost. All costs depend on quality and/or reliability. The key to our approach is the calculation of the so-called system cumulative distribution function (time-dependent probability of failure). For that we use an equivalent time-invariant “composite” limit state which is accurate for monotonic or non-monotonic in time, systems. Examples highlight the calculation of the cumulative distribution function and the design methodology for lifecycle cost.